Estimation of large covariance matrices via free deconvolution: computational and statistical aspects
Probability
2023-05-10 v1 Statistics Theory
Computation
Statistics Theory
Abstract
The estimation of large covariance matrices has a high dimensional bias. Correcting for this bias can be reformulated via the tool of Free Probability Theory as a free deconvolution. The goal of this work is a computational and statistical resolution of this problem. Our approach is based on complex-analytic methods methods to invert -transforms. In particular, one needs a theoretical understanding of the Riemann surfaces where multivalued transforms live and an efficient computational scheme.
Keywords
Cite
@article{arxiv.2305.05646,
title = {Estimation of large covariance matrices via free deconvolution: computational and statistical aspects},
author = {Reda Chhaibi and Fabrice Gamboa and Slim Kammoun and Mauricio Velasco},
journal= {arXiv preprint arXiv:2305.05646},
year = {2023}
}
Comments
v1: Preliminary version